{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3nuYd8jPLFhT"
   },
   "source": [
    "##### Copyright 2020 The TensorFlow Authors.\n",
    "\n",
    "Licensed under the Apache License, Version 2.0 (the \"License\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "HGjGIBkBLFhU"
   },
   "outputs": [],
   "source": [
    "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "# https://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "V33An_hTR-12"
   },
   "source": [
    "# Chapter 3 - Sampling the Imaginary\n",
    "\n",
    "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/statistical_rethinking/notebooks/03_sampling_the_imaginary\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/statistical_rethinking/notebooks/03_sampling_the_imaginary.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/statistical_rethinking/notebooks/03_sampling_the_imaginary.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/examples/statistical_rethinking/notebooks/03_sampling_the_imaginary.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "e-oEYYBtR-15"
   },
   "source": [
    "## Imports and utility functions\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "DqPexYsLLFhb"
   },
   "outputs": [],
   "source": [
    "#@title Install { display-mode: \"form\" }\n",
    "TF_Installation = 'System' #@param ['TF Nightly', 'TF Stable', 'System']\n",
    "\n",
    "if TF_Installation == 'TF Nightly':\n",
    "  !pip install -q --upgrade tf-nightly\n",
    "  print('Installation of `tf-nightly` complete.')\n",
    "elif TF_Installation == 'TF Stable':\n",
    "  !pip install -q --upgrade tensorflow\n",
    "  print('Installation of `tensorflow` complete.')\n",
    "elif TF_Installation == 'System':\n",
    "  pass\n",
    "else:\n",
    "  raise ValueError('Selection Error: Please select a valid '\n",
    "                   'installation option.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "9hEWxUXrLFhf"
   },
   "outputs": [],
   "source": [
    "#@title Install { display-mode: \"form\" }\n",
    "TFP_Installation = \"System\" #@param [\"Nightly\", \"Stable\", \"System\"]\n",
    "\n",
    "if TFP_Installation == \"Nightly\":\n",
    "  !pip install -q tfp-nightly\n",
    "  print(\"Installation of `tfp-nightly` complete.\")\n",
    "elif TFP_Installation == \"Stable\":\n",
    "  !pip install -q --upgrade tensorflow-probability\n",
    "  print(\"Installation of `tensorflow-probability` complete.\")\n",
    "elif TFP_Installation == \"System\":\n",
    "  pass\n",
    "else:\n",
    "  raise ValueError(\"Selection Error: Please select a valid \"\n",
    "                   \"installation option.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "cMzcPgVtR-16"
   },
   "outputs": [],
   "source": [
    "#@title Install { display-mode: \"form\" }\n",
    "\n",
    "# Install packages that are not installed in colab\n",
    "try:\n",
    "  import google.colab\n",
    "  IN_COLAB = True\n",
    "except:\n",
    "  IN_COLAB = False\n",
    "\n",
    "if IN_COLAB:\n",
    "  import sys\n",
    "  if sys.executable:  # make sure pip is available\n",
    "    print(\"Installing arviz ...\")\n",
    "    !{sys.executable} -m pip install -q arviz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "RF7a5tCaR-2K",
    "outputId": "72b65793-5800-43fc-b3a1-64dd58cdb643"
   },
   "outputs": [],
   "source": [
    "# Core\n",
    "import numpy as np\n",
    "import arviz as az\n",
    "import pandas as pd\n",
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "import scipy.stats as stats\n",
    "\n",
    "# visualization \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# aliases\n",
    "tfd = tfp.distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "hIPc5oJQLFhq"
   },
   "outputs": [],
   "source": [
    "az.style.use('seaborn-colorblind')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VzHqoXwtR-2m"
   },
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vMt0Fb_oR-2n"
   },
   "source": [
    "We are interested in a blood test that correctly detects vampirisim 95% of time:\n",
    "\n",
    "$$\\operatorname{Pr}(\\text{Positive}|\\text{Vampire}) = 0.95$$\n",
    "\n",
    "The test has a false positive rate of:\n",
    "\n",
    "$$\\operatorname{Pr}(\\text{Positive}|\\text{Mortal}) = 0.01$$\n",
    "\n",
    "We also know that vampires are rare--about 0.1% of population:\n",
    "\n",
    "$$\\operatorname{Pr}(\\text{Vampire}) = 0.001$$\n",
    "\n",
    "To compute $\\operatorname{Pr}(\\text{Vampire}|\\text{Positive})$ we will apply Bayes' rule:\n",
    "\n",
    "$$\n",
    "\\operatorname{Pr}(\\text{Vampire}|\\text{Positive})  = \\frac{\\operatorname{Pr}(\\text{Positive}|\\text{Vampire}) \\operatorname{Pr}(\\text{Vampire})}{\\operatorname{Pr}(\\text{Positive})}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "20qfjf_fR-2o"
   },
   "source": [
    "##### Code 3.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "E3ascQZwR-2q",
    "outputId": "a895442a-cb91-4f5d-d257-fc3ecbfc258e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08683729433272395"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pr_Positive_Vampire = 0.95\n",
    "Pr_Positive_Mortal = 0.01\n",
    "Pr_Vampire = 0.001\n",
    "tmp = Pr_Positive_Vampire * Pr_Vampire\n",
    "Pr_Positive = tmp + Pr_Positive_Mortal * (1 - Pr_Vampire)\n",
    "Pr_Vampire_Positive = tmp / Pr_Positive\n",
    "Pr_Vampire_Positive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uc665rPKR-2w"
   },
   "source": [
    "This result shows that there is only 8.7% chance that suspect is vampire even if the test is positive, because of the low incidence rate (prior probability)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uiKda961R-2x"
   },
   "source": [
    "## 3.1 Sampling from a grid-approximate posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UNu7Ql7IR-2z"
   },
   "source": [
    "##### Code 3.2\n",
    "\n",
    "Let's compute the posterior for the globe tossing model, the probability of *p* conditional on the data: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "VccHwZjoR-20"
   },
   "outputs": [],
   "source": [
    "p_grid = tf.linspace(start=0., stop=1., num=1000)\n",
    "prob_p = tf.ones(1000)\n",
    "prob_data = tfd.Binomial(total_count=9, probs=p_grid).prob(6)\n",
    "joint_prob = prob_data * prob_p\n",
    "posterior = joint_prob / tf.reduce_sum(joint_prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qvLgHilaR-26"
   },
   "source": [
    "\n",
    "\n",
    "We now wish to draw 10000 samples from the posterior :\n",
    "\n",
    "##### Code 3.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "4nKQJLZiR-27"
   },
   "outputs": [],
   "source": [
    "samples = tfd.Categorical(probs=posterior).sample(10_000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "O-9wh9ZxR-3E"
   },
   "source": [
    "Now let's display the resulting samples:\n",
    "\n",
    "##### Code 3.4\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 295
    },
    "id": "QAKYs5ZXR-3G",
    "outputId": "ad4a04b6-6dc2-4983-db97-407fd1077091"
   },
   "outputs": [
    {
     "data": {
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LGbm+GAd0LjTO5eLpz3btpmo2NcvbcD2XO/vpSVIvIM5VHlezPH44Xefp+RYHl9o0neTl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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_rows = p_grid.numpy()[samples]\n",
    "_, ax = plt.subplots()\n",
    "ax.scatter(range(len(sample_rows)), sample_rows, alpha=0.2)\n",
    "ax.set(ylabel='proportion water (p)',\n",
    "       xlabel='sample number',\n",
    "       title='Figure 3.1 (left panel)',\n",
    "       ylim=(0, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7WMQQvNQR-3L"
   },
   "source": [
    "As the plot shows, there are many samples in the 0.6 region and very few below 0.25."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eXI4sm3YR-3M"
   },
   "source": [
    "\n",
    "Here's the density estimate of these samples, which is very similar to the ideal posterior you computed via grid approximation in Chapter 2, section 2.4.3.\n",
    "\n",
    "##### Code 3.5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 313
    },
    "id": "VcHmWurgR-3O",
    "outputId": "c8c049db-9c49-432b-adee-1c4b64d47b6c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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w4eHhiIuL45lipNcEQcD7+6/D3sIY7/XnNUvUsiYFOWNDeBoOXM/GcwFOYsfR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\nIiLSSSw4IiLSSSw4IiLSSf8HtloCJeaDvocAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax, = az.plot_density(sample_rows, credible_interval=1.)\n",
    "ax.set(title=\"Figure 3.1 (right panel)\",\n",
    "       xlabel=\"proportion water (p)\",\n",
    "       ylabel=\"Density\",\n",
    "       xlim=(0, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D_sGUGSWR-3U"
   },
   "source": [
    "## 3.2 Sampling to summarize\n",
    "\n",
    "Once we have the posterior distribution the next step is to summarize it. Some of the common tasks are:\n",
    "\n",
    ">* How much posterior probability lies below some parameter value?\n",
    "* How much posterior probability lies between two parameter values?\n",
    "* Which parameter value marks the lower 5% of the posterior probability?\n",
    "* Which range of parameter values contains 90% of the posterior probability? \n",
    "* Which parameter value has highest posterior probability?\n",
    "\n",
    ">These simple questions can be usefully divided into questions about (1) intervals of defined boundaries, (2) questions about intervals of defined probability mass, and (3) questions about point estimates. We’ll see how to approach these questions using samples from the posterior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5v8l9cDOR-3V"
   },
   "source": [
    "### 3.2.1 Intervals of defined boundaries\n",
    "\n",
    "What is the posterior probability that proportion of water is less than 0.5?  We can simply sum all of the probabilities where the parameter value is less than 0.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d-yLKJceR-3W"
   },
   "source": [
    "Let's add up the posterior probability where p < 0.5:\n",
    "\n",
    "##### Code 3.6\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "OKK9FiINR-3X",
    "outputId": "12bb17e0-b9ca-4078-977d-69639f1b92b6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(), dtype=float32, numpy=0.1718746>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.reduce_sum(posterior[p_grid < 0.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3mMvqOKmR-3b"
   },
   "source": [
    "This means that about 17% of posterior probability is below 0.5.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "H3iM1BInR-3c"
   },
   "source": [
    "Now let's find the frequency of parameter values below 0.5:\n",
    "\n",
    "##### Code 3.7\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "cKbf6goIR-3d",
    "outputId": "b70c8bc2-f29e-4632-ffd9-a4b9088bc8d5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1731"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.where(sample_rows < 0.5).shape[0] / 10_000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ag1KvKOCR-3m"
   },
   "source": [
    "This is nearly the same answer as that of grid approximation, in Code 3.6,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7KpXBOi1R-3n"
   },
   "source": [
    "Using the same approach, how much posterior probability lies between 0.5 and 0.75?\n",
    "\n",
    "##### Code 3.8\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "YkltM9HyR-3o",
    "outputId": "cade552d-9494-43cc-e65c-ab93fd23614a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(), dtype=float32, numpy=0.6045>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition = (sample_rows > 0.5) & (sample_rows < 0.75)\n",
    "tf.reduce_sum(tf.cast(condition, float))/ 10_000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UEpbVzf-R-3u"
   },
   "source": [
    "### 3.2.2 Intervals of defined mass\n",
    "\n",
    "Scientific journals will commonly report on an \"interval of defined mass\" also known as a *Confidence Interval*. The text will use the term *Compatiblity Interval* instead, since the interval indicates a range of parameter values *compatible* with the model and data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Sa2X4HnoR-3v"
   },
   "source": [
    "If we want to know what interval of parameter values contains 80% of the probability mass, we can simply examine the samples from the posterior, with an interval starting at *p*=0 until we have reached the 80th percentile.\n",
    "\n",
    "##### Code 3.9\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "u6q7fbtRR-3y",
    "outputId": "5d89d3d8-95c3-4b8a-c7f7-f4867b589cf4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(), dtype=float32, numpy=0.7597597>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfp.stats.percentile(sample_rows, q=80.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KaSBqySER-34"
   },
   "source": [
    "\n",
    "Similarly, the middle 80% interval lies between the 10th percentile and the 90th percentile:\n",
    "\n",
    "##### Code 3.10\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "ZSF8P2ksR-35",
    "outputId": "2226b963-b1e5-4bfc-9fa8-e9af2e4037d4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(2,), dtype=float32, numpy=array([0.44844845, 0.8108108 ], dtype=float32)>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfp.stats.percentile(sample_rows, q=[10.,90.])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mBwVThXvR-39"
   },
   "source": [
    "The text refers to intervals like this, which assign equal probability mass to each tail, as *Percentile Intervals*. They can be useful to characterize a distribution if it is fairly symmetrical. \n",
    "\n",
    "By contrast, consider a highly skewed distribution with a maximum value at *p*=1, like the posterior for observing three waters in three tosses with a uniform prior. We can compute this posterior using grid approximation:\n",
    "\n",
    "##### Code 3.11\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "X8VNpMLiR-3-"
   },
   "outputs": [],
   "source": [
    "p_grid = tf.linspace(start=0., stop=1., num=1000)\n",
    "prior = tf.ones(1000)\n",
    "likelihood = tfd.Binomial(total_count=3, probs=p_grid).prob(3)\n",
    "joint_prob = likelihood * prior\n",
    "posterior = joint_prob / tf.reduce_sum(joint_prob)\n",
    "\n",
    "samples = tfd.Categorical(probs=posterior).sample(10_000)\n",
    "sample_rows = p_grid.numpy()[samples]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kt_hdKyzR-4B"
   },
   "source": [
    "Let's compute a 50% percentile compatibility interval that provides the central 50% probability by assigning 25% of the probability below the interval, and 25% above it:\n",
    "\n",
    "##### Code 3.12\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "dsRLAsSgR-4C",
    "outputId": "37cf8741-de48-4576-f1ea-9e5a82b52914"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(2,), dtype=float32, numpy=array([0.7097097, 0.9299299], dtype=float32)>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfp.stats.percentile(sample_rows, q=[25.,75.])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SQLv2ubaR-4G"
   },
   "source": [
    "Given the assymetric shape of the distribution, this interval is misleading because it fails to contain the most probable parameter values at *p*=1.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "k9Y_OvNVR-4H"
   },
   "source": [
    "The *Highest Posterior Density Interval* (HPDI) is the narrowest interval containing the specified probability mass, which always contains the most probable parameter value.\n",
    "\n",
    "We can use arviz to compute it:\n",
    "\n",
    "##### Code 3.13\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "eZBumJuiR-4I",
    "outputId": "295f6d20-e85e-4131-97f7-abeeb72be2a8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.8418418, 1.       ], dtype=float32)"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.hpd(sample_rows, credible_interval=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kBYEz8ztR-4N"
   },
   "source": [
    "### 3.2.3 Point Estimates\n",
    "\n",
    "How can we use the posterior distribution to create a point estimate to summarize the distribution for getting three waters from three tosses? Let's compare three different types of point estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PvtPAI_AR-4O"
   },
   "source": [
    "##### Code 3.14\n",
    "\n",
    "The *maximum a posteriori* (MAP) estimate is the parameter value with the high posterior probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "k_W1DZgBR-4P",
    "outputId": "bbe9f77b-27b2-4d6b-e035-2a45255d7139"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1,), dtype=float32, numpy=array([1.], dtype=float32)>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_grid[posterior == max(posterior)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cN0MfWq6R-4T"
   },
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "With our samples from the posterior, we can approximate the MAP:\n",
    "##### Code 3.15\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "CrNSZo2rR-4U",
    "outputId": "75b3d90d-3ad6-4e4c-c338-11c365c28186"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(), dtype=float32, numpy=1.0>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.reduce_max(sample_rows)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "E4Df7GOOR-4X"
   },
   "source": [
    "We can also compute the posterior mean and median.\n",
    "\n",
    "##### Code 3.16\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "8HpNbzd3R-4Y",
    "outputId": "6f09f5fa-af9b-4e5c-e4d5-39d440d872be"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean=0.799774, median=0.841842\n"
     ]
    }
   ],
   "source": [
    "median = tfp.stats.percentile(sample_rows, q=50.)\n",
    "mean = tf.math.reduce_mean(sample_rows)\n",
    "\n",
    "print(f\"mean={mean:.6f}, median={median:.6f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JkAbVtN4R-4c"
   },
   "source": [
    "We can use a loss function to compute the cost of using any specific point estimate. Suppose our loss function is proportional to the difference between our decision (e.g., our point estimate) and the true value of the parameter.\n",
    "\n",
    "If we chose *p*=0.5 as our decision for the parameter value, we can use the posterior distribution to compute the expected loss, by computing the weighted average loss: We weight each loss by its corresponding posterior probability:\n",
    "\n",
    "\n",
    "##### Code 3.17\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "oOrwlpCvR-4c",
    "outputId": "9f20797d-da75-4636-a171-ffdf32f37eb2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(), dtype=float32, numpy=0.31287518>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.reduce_sum(posterior * abs(0.5 - p_grid))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HGETHvmxR-4f"
   },
   "source": [
    "We can repeat this loss computation for every possible decision:\n",
    "##### Code 3.18\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "fNkSz11iR-4g"
   },
   "outputs": [],
   "source": [
    "loss = tf.map_fn(lambda d: tf.reduce_sum(posterior * np.abs(d - p_grid)), p_grid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ux2nQxwXR-4k"
   },
   "source": [
    "##### Code 3.19\n",
    "\n",
    "Now, we can find the parameter value that minimizes the loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "k2vEVVPgR-4k",
    "outputId": "6427e400-66f4-42a6-9561-a23ba139f948"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(), dtype=float32, numpy=0.8408408>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_grid[tf.math.argmin(loss)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "62HS0I6rR-4o"
   },
   "source": [
    "It turns out that the value that minimizes our loss will be the same as that for the posterior median, which splits the posterior density so that half the mass is above it, with half below it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fTR3IhT_R-4p"
   },
   "source": [
    "## 3.3 Sampling to simulate prediction\n",
    "\n",
    "\n",
    "We can use our Bayesian models to produce simulated observations, since all Bayesian models are generative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "oqPdGSsyR-4p"
   },
   "source": [
    "### 3.3.1 Dummy data\n",
    "\n",
    ">We will call such simulated data *dummy data*, to indicate that it is a stand-in for actual data.\n",
    "\n",
    "Recall from the globe tossing model that the probability of observing *W* counts of water in *N* tosses with proportion of water *p* is given by the binomial likelihood:\n",
    "\n",
    "$$\n",
    "\\operatorname{Pr}(W|N,p) = \\frac{N!}{W!(N-W)!}p^W(1-p)^{N-W}\n",
    "$$\n",
    "\n",
    "For two tosses of the globe and proportion of water at 0.7 we can compute the probability of observing 0, 1, and 2 counts of water:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3EMtUcwxR-4q"
   },
   "source": [
    "##### Code 3.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "R3JigMx5R-4r",
    "outputId": "9430101a-c3b6-4c33-fb8a-ef636afe2cdf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([0.09      , 0.42000002, 0.48999998], dtype=float32)>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfd.Binomial(total_count=2, probs=0.7).prob(np.arange(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CRYsZq_GR-4u"
   },
   "source": [
    "This means that there’s a 9% chance of observing *w* = 0, a 42% chance of *w* = 1, and a 49% chance of *w* = 2.\n",
    "\n",
    "We can simulate a dummy observation of *W* from our model by sampling from the binomial distribution:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "o7pf5MQgR-4u"
   },
   "source": [
    "##### Code 3.21\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "XKCHYg-OR-4v",
    "outputId": "4f4cdca7-ac10-4bef-f1ff-383de80ef83a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(), dtype=float32, numpy=1.0>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfd.Binomial(total_count=2, probs=0.7).sample()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3c5vqJO-O9cv"
   },
   "source": [
    "The result is the number of water observations in 2 tosses of the globe.\n",
    "\n",
    "A set of 10 simulations can be made by:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1h4np4S8R-4y"
   },
   "source": [
    "##### Code 3.22\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "LITo0fAJR-4z",
    "outputId": "0c835355-a6b5-43af-ea87-0f00869eb44b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(10,), dtype=float32, numpy=array([2., 2., 1., 2., 1., 2., 2., 1., 2., 1.], dtype=float32)>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfd.Binomial(total_count=2, probs=0.7).sample(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lmHNBqtnR-43"
   },
   "source": [
    "\n",
    "When we generate 100,000 dummy observations, note that each value of *w* appears in proportion to its likelihood\n",
    "\n",
    "##### Code 3.23\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "W3nDiWihR-44",
    "outputId": "ee1baded-56b6-4168-924e-564e9b2a0288"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float64, numpy=array([0.08983, 0.41984, 0.49033])>"
      ]
     },
     "execution_count": 0,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_w = tfd.Binomial(total_count=2, probs=0.7).sample(100_000)\n",
    "\n",
    "tf.unique_with_counts(tf.sort(dummy_w)).count / int(1e5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8-mjlykER-48"
   },
   "source": [
    ">Only two tosses of the globe isn’t much of a sample, though. So now let’s simulate the same sample size as before, 9 tosses.\n",
    "\n",
    "##### Code 3.24\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 283
    },
    "id": "Ps_mwAYnLFjJ",
    "outputId": "9499e3e8-31a2-4518-94a9-afcd9cbcaf35"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EpP3z+66wrVu3kpmZCcC6desYPXq073koIiIip/j9oK/t27cTFhYGND+f5dZbb+XFF18M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\nf/zjH31t+fn5jBk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      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dummy_w = tfd.Binomial(total_count=9, probs=0.7).sample((100000,))\n",
    "_, ax = plt.subplots()\n",
    "ax.hist(dummy_w.numpy(), bins=np.arange(11), rwidth=0.2)\n",
    "ax.set(xlabel=\"dummy water count\", \n",
    "       ylabel=\"Frequency\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_AxV9mFGWGNt"
   },
   "source": [
    "### 3.3.2. Model Checking\n",
    "\n",
    ">We’d like to propagate the parameter uncertainty—carry it forward—as we evaluate the implied predictions. All that is required is averaging over the posterior density for *p*, while computing the predictions. For each possible value of the parameter *p*, there is an implied distribution of outcomes. So if you were to compute the sampling distribution of outcomes at each value of *p*, then you could average all of these prediction distributions together, using the posterior probabilities of each value of *p*, to get a POSTERIOR PREDICTIVE DISTRIBUTION.\n",
    "\n",
    "To simulate predicted observations for nine globe tosses, for a single value of *p*=0.6, we can use `Binomial` to generate random binomial samples:\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5HchgmkaR-5B"
   },
   "source": [
    "##### Code 3.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "9pp-X5h-R-5B"
   },
   "outputs": [],
   "source": [
    "w = tfd.Binomial(total_count=9, probs=0.6).sample(1e4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "go8zHTQ1R-5F"
   },
   "source": [
    ">All you need to propagate parameter uncertainty into these predictions is replace the value 0.6 with samples from the posterior.... Since the sampled values appear in proportion to their posterior probabilities, the resulting simulated observations are averaged over the posterior.\n",
    "\n",
    "##### Code 3.26"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "id": "Bgn_UI3mR-5G"
   },
   "outputs": [],
   "source": [
    "w = tfd.Binomial(total_count=9, probs=sample_rows).sample()"
   ]
  }
 ],
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